# Finding an upper bound for error. Taylor polynomial

Here $$p_3(x)=-1+2(x-1)+0+(e(x-1)^3)/6.$$

What I have done

since |$$f^4$$ (w)| <= M

1/2 <= f <= 1

1/16<=M <=1

I applied the Taylor remainder formula

What im not sure about is the value of M. Since im calculating upper bound, I let M =1 and x=1/2 as given.

I believe I calculated the Taylor error but what do I do now to find the upper error. Is there a formula for this?

Is this the right way of approaching this question?

• What book are you using? – Jack Aug 3 at 0:28
• @Jack Hi using James Stewart calculus 8th edition. I believe the formula is universal for all books? – DDDDOO Aug 3 at 0:37
• I don't see this exercise in Stewart's book. Is part (a) this question of yours? – Jack Aug 3 at 0:54
• @Jack. This is from a supplementary worksheet. This question is part of many and I want to check if I am working correctly as if I can do this one correctly I can apply to the other questions which are similar. – DDDDOO Aug 3 at 0:59
• I can't make sense the first sentence right after "what I have done". Where is the inquality $1/2\le M\le 1$ from? – Jack Aug 3 at 1:03